I've lived aboard in BC year round, for decades, in extreme comfort. The trick is lots of foam insulation sprayed into my steel hull. Any piece of steel the size of your fingernail which is not covered by at least a half inch of foam will drip like a leaky faucet. I believe fibrglass is not much different in that regard . A friend who sold his spray foamed steel boat and bought a fibreglass one said living in the fibreglass hull was like living in a block of ice, by comparison.So the trick is start cutting and gluing in foam, a bit at a time. The thicker the better. You can do it over time and each piece of foam you glue in will improve the comfort level.
A false ceiling with an open air space is not much insulation, and wont do much.
Brent Swain, Yacht designer, Builder, and author of "Origami Metal Boatbuilding"